Circular vertical hall (CVH) sensing element with signal processing and arctangent function

ABSTRACT

A magnetic field sensor includes a circular vertical Hall (CVH) sensing element to produce a signal representing an external magnetic field as detected by the CVH sensing element, a sigma-delta analog-to-digital converter to generate a converted signal, modulators to produce quadrature modulated signals from the converted signal, and a processor to produce an estimated angle of the external magnetic field using the quadrature modulated signals. An arctangent function may be used to calculate the estimated angle. A sliding window integration scheme may be used over one or more CVH cycles.

FIELD OF THE INVENTION

This invention relates generally to electronic circuits, and, moreparticularly, to an electronic circuit that can process signals from acircular vertical Hall (CVH) sensing element to determine an angle of amagnetic field using particular processing techniques.

BACKGROUND OF THE INVENTION

Sensing elements are used in a variety of applications to sensecharacteristics of an environment. Sensing elements include, but are notlimited to, pressure sensing elements, temperature sensing elements,light sensing elements, acoustic sensing elements, and magnetic fieldsensing elements.

A magnetic field sensor can include one or more magnetic field sensingelements and also other electronics.

Magnetic field sensors can be used in a variety of applications. In oneapplication, a magnetic field sensor can be used to detect a directionof a magnetic field. In another application, a magnetic field sensor canbe used to sense an electrical current. One type of current sensor usesa Hall effect magnetic field sensing element in proximity to acurrent-carrying conductor.

Planar Hall elements and vertical Hall elements are known types ofmagnetic field sensing elements that can be used in magnetic fieldsensors. A planar Hall element tends to be responsive to magnetic fieldperpendicular to a surface of a substrate on which the planar Hallelement is formed. A vertical Hall element tends to be responsive tomagnetic field parallel to a surface of a substrate on which thevertical Hall element is formed.

SUMMARY OF THE INVENTION

In an embodiment, a magnetic field sensor comprises a circular verticalHall (CVH) sensing element to produce an analog signal representing anexternal magnetic field; an analog-to-digital converter coupled toreceive the analog signal and produce a digital signal; an quadraturemodulator circuit coupled to the digital signal and operable to generatea plurality of quadrature modulated signals; and a processor stagecoupled to receive signals representative of the plurality of quadraturemodulated signals and operable to perform an arctangent calculation tocompute an estimated angle of the external magnetic field.

One or more of the following features may be included.

The processor stage may include a circuit to perform a CORDIC algorithm.The circuit to perform the CORDIC algorithm may be a processorconfigured to execute instructions that cause the processor to performthe CORDIC algorithm. The instructions may be software instructions,firmware instructions, micro-code instructions, or a combinationthereof. The arctangent calculation may produce an estimated angle hasan accuracy greater than a predetermined angle between one or morevertical Hall element contacts of the CVH sensing element.

The analog-to-digital converter may be a sigma-delta analog-to-digitalconverter and the digital signal is a pulse stream. The sigma-deltaanalog-to-digital converter may include a noise shaping transform thatshifts quantization noise to higher frequencies.

The processor stage may be further configured to perform a slidingwindow integration using the signals representative of the plurality ofquadrature modulated signals. The processor stage may be configured toperform the arctangent calculation to compute the estimated angle at afrequency greater than that of a CVH cycle.

The quadrature modulator circuit may be configured to produce a firstmodulated signal that is modulated with a cosine function and a secondmodulated signal that is modulated with a sine function.

The processor stage may be configured to calculate a quotient of thefirst modulated signal divided by the second modulated signal. Theprocessor stage may be configured to perform the arctangent calculationusing the quotient.

In another embodiment, a method comprises detecting a magnetic field bya circular vertical Hall (CVH) sensing element; producing, by the CVHsensing element, an analog signal representing the external magneticfield; converting the analog signal to a digital signal; generating aplurality of quadrature modulated signals; and performing an arctangentcalculation to compute an estimated angle of the external magneticfield.

One or more of the following features may be included.

Performing the arctangent calculation may comprise performing a CORDICalgorithm. The CORDIC algorithm may be performed by a processorconfigured to execute instructions that cause the processor to performthe CORDIC algorithm. The instructions may be software instructions,firmware instructions, micro-code instructions, or a combination thereof

Performing the arctangent calculation may include producing an estimatedangle that has an accuracy greater than a predetermined angle betweenone or more vertical Hall element contacts of the CVH sensing element.

Converting the analog signal may include generating a sigma-deltaencoded N-bit stream representing the analog signal. Converting theanalog signal may comprise applying a noise shaping transform to theanalog signal that shifts quantization noise to higher frequencies.

The method may include performing a sliding window integration using theplurality of quadrature modulated signals and/or performing thearctangent calculation to compute the estimated angle. Generating theplurality of quadrature signals may comprise modulating a first signalwith a cosine function to produce a first modulated signal andmodulating a second signal with a sine function to produce a secondmodulated signal.

A quotient of the first modulated signal divided by the second modulatedsignal may be calculated. The arctangent calculation may includeperforming the arctangent calculation using the quotient.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the invention, as well as the invention itselfmay be more fully understood from the following detailed description ofthe drawings, in which:

FIG. 1 is a pictorial showing a circular vertical Hall (CVH) sensingelement having a plurality of vertical Hall elements arranged in acircle over a common implant region and a two pole magnet disposed closeto the CVH sensing element.

FIG. 2 is a graph showing an output signal as may be generated by theCVH sensing element of FIG. 1.

FIG. 3 is a block diagram of a magnetic field sensor having a CVHsensing element, having an analog-to-digital converter and a processorcircuit that can include an integrator circuit.

FIG. 3A is a block diagram of an integrator circuit that can be used asthe integrator circuit of the magnetic field sensor of FIG. 3.

FIG. 3B is a block diagram of another embodiment of an integratorcircuit that can be used as the integrator circuit of the magnetic fieldsensor of FIG. 3.

FIG. 4 is a graph showing a frequency spectrum of the output of ananalog-to-digital converter that can be generated by theanalog-to-digital converter of the magnetic field sensor of FIG. 3.

FIG. 5 is a block diagram of a processor circuit that can be used as theprocessor circuit of the magnetic field sensor of FIG. 3.

FIG. 6 is a pictorial showing a circular vertical Hall (CVH) andillustrating sliding window integration cycles.

FIG. 7 is a block diagram of an integrator circuit that performs slidingwindow integration and that circuit that can be used as the integratorcircuit of the magnetic field sensor of FIG. 3.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, the term “magnetic field sensing element” is used todescribe a variety of electronic elements that can sense a magneticfield. The magnetic field sensing element can be, but is not limited to,a Hall Effect element, a magnetoresistance element, or amagnetotransistor. As is known, there are different types of Hall Effectelements, for example, a planar Hall element, a vertical Hall element,and a Circular Vertical Hall (CVH) element. As is also known, there aredifferent types of magnetoresistance elements, for example, asemiconductor magnetoresistance element such as Indium Antimonide(InSb), a giant magnetoresistance (GMR) element, an anisotropicmagnetoresistance element (AMR), a tunneling magnetoresistance (TMR)element, a magnetic tunnel junction (MTJ), a spin-valve, etc. Themagnetic field sensing element may be a single element or,alternatively, may include two or more magnetic field sensing elementsarranged in various configurations, e.g., a half bridge or full(Wheatstone) bridge. Depending on the device type and other applicationrequirements, the magnetic field sensing element may be a device made ofa type IV semiconductor material such as Silicon (Si) or Germanium (Ge),or a type III-V semiconductor material like Gallium-Arsenide (GaAs) oran Indium compound, e.g., Indium-Antimonide (InSb).

Some of the above-described magnetic field sensing elements tend to havean axis of maximum sensitivity parallel to a substrate that supports themagnetic field sensing element, and others of the above-describedmagnetic field sensing elements tend to have an axis of maximumsensitivity perpendicular to a substrate that supports the magneticfield sensing element. In particular, planar Hall elements tend to haveaxes of sensitivity perpendicular to a substrate, while metal based ormetallic magnetoresistance elements (e.g., GMR, TMR, AMR, spin-valve)and vertical Hall elements tend to have axes of sensitivity parallel toa substrate.

It will be appreciated by those of ordinary skill in the art that whilea substrate (e.g. a semiconductor substrate) is described as“supporting” the magnetic field sensing element, the element may bedisposed “over” or “on” the active semiconductor surface, or may beformed “in” or “as part of” the semiconductor substrate, depending uponthe type of magnetic field sensing element. For simplicity ofexplanation, while the embodiments described herein may utilize anysuitable type of magnetic field sensing elements, such elements will bedescribed here as being supported by the substrate.

As used herein, the term “magnetic field sensor” is used to describe acircuit that uses a magnetic field sensing element, generally incombination with other circuits. Magnetic field sensors are used in avariety of applications, including, but not limited to, an angle sensorthat senses an angle of a direction of a magnetic field, a currentsensor that senses a magnetic field generated by a current carried by acurrent-carrying conductor, a magnetic switch that senses the proximityof a ferromagnetic object, a rotation detector that senses passingferromagnetic articles, for example, magnetic domains of a ring magnetor a ferromagnetic target (e.g., gear teeth) where the magnetic fieldsensor is used in combination with a back-biased or other magnet, and amagnetic field sensor that senses a magnetic field density of a magneticfield.

As used herein, the term “target” is used to describe an object to besensed or detected by a magnetic field sensor or magnetic field sensingelement. A target may be ferromagnetic or magnetic.

As is known in the art, magnetic fields have direction and strength. Thestrength of a magnetic field can be described as a magnitude of amagnetic flux or flux density. Therefore, the terms magnetic field“strength” and magnetic “flux” may be used interchangeably in thisdocument.

As used herein, the term “ground” refers to a reference potential in anelectrical circuit from which other voltages are measured, or a commonreturn path for electrical current. Ground may also refer to a portionof a circuit that is connected to earth ground.

Referring to FIG. 1, a circular vertical Hall (CVH) sensing element 12includes a common circular implant region 18 having a plurality ofvertical Hall elements disposed thereon, of which a vertical Hallelement 12 a is but one example. Each vertical Hall element has aplurality of Hall element contacts (e.g., four or five contacts), ofwhich a vertical Hall element contact 12 aa is but one example.

The term “common” circular implant region indicates that the pluralityof vertical Hall elements of the CVH sensing element can have nodiffused barriers between the plurality of vertical Hall elements.

A particular vertical Hall element (e.g., 12 a) within the CVH sensingelement 12, which, for example, can have five adjacent contacts, canshare some, for example, four, of the five contacts with a next verticalHall element (e.g., 12 b). Thus, a next vertical Hall element can beshifted by one contact from a prior vertical Hall element. For suchshifts by one contact, it will be understood that the number of verticalHall elements is equal to the number of vertical Hall element contacts,e.g., 32. However, it will also be understood that a next vertical Hallelement can be shifted by more than one contact from the prior verticalHall element, in which case, there are fewer vertical Hall elements thanthere are vertical Hall element contacts in the CVH sensing element.

A center of a vertical Hall element 0 is positioned along an x-axis 20and a center of vertical Hall element 8 is positioned along a y-axis 22.In the example shown in FIG. 1, there are thirty-two vertical Hallelements and thirty-two vertical Hall element contacts. However, a CVHsensing element can have more than or fewer than thirty-two verticalHall elements and more than or fewer than thirty-two vertical Hallelement contacts.

In some applications, a circular magnet 14 having a south side 14 a anda north side 14 b can be disposed over the CVH sensing element 12. Thecircular magnet 14 may generate a magnetic field 16 having a directionfrom the north side 14 b to the south side 14 a, here shown to bepointed to a direction of about forty-five degrees relative to x-axis20. Other magnets having other shapes and configurations are possible.

In some applications, the circular magnet 14 is mechanically coupled toa rotating object (a target object), for example, an automobilecrankshaft or an automobile camshaft, and is subject to rotationrelative to the CVH sensing element 12. With this arrangement, the CVHsensing element 12 in combination with an electronic circuit describedbelow can generate a signal related to the angle of rotation of themagnet 14.

Referring now to FIG. 2, a graph 200 has a horizontal axis with a scalein units of CVH vertical Hall element position, n, around a CVH sensingelement, for example, the CVH sensing element 12 of FIG. 1. The graph200 also has a vertical axis with a scale in units of amplitude in unitsof millivolts. The vertical axis is representative of output signallevels from the plurality of vertical Hall elements of the CVH sensingelement.

The graph 200 includes a signal 202 representative of output signallevels from the plurality of vertical Hall elements of the CVH takensequentially with the magnetic field 16 of FIG. 1 stationary andpointing in a direction of forty-five degrees.

The graph 200 shows one CVH sensing element cycle, i.e. one revolutionof the CVH sensing element where each Hall element is activated insequence around the circumference of the CVH sensing element. Forexample, the portion of signal 202 shown in graph 200 is produced duringone CVH cycle as each of the Hall elements are activated around thecircumference of the CVH sensing element. In this example, the CVH cyclestarts with Hall element position 0, and ends with Hall element position31. Of course, in this example, a CVH cycle can have any start and endpoint as long as the CVH cycle includes one revolution of the CVHsensing element.

Referring briefly to FIG. 1, as described above, vertical Hall element 0is centered along the x-axis 20 and vertical Hall element 8 is centeredalong the y-axis 22. In the exemplary CVH sensing element 12, there arethirty-two vertical Hall element contacts and a corresponding thirty-twovertical Hall elements, each vertical Hall element having a plurality ofvertical Hall element contacts, for example, five contacts.

In FIG. 2, a maximum positive signal is achieved from a vertical Hallelement centered at position 4, which is aligned with the magnetic field16 of FIG. 1, such that a line drawn between the vertical Hall elementcontacts (e.g., five contacts) of the vertical Hall element at position4 is perpendicular to the magnetic field 16. A maximum negative signalis achieved from a vertical Hall element centered at position 20, whichis also aligned with the magnetic field 16 of FIG. 1, such that a linedrawn between the vertical Hall element contacts (e.g., five contacts)of the vertical Hall element at position 20 is also perpendicular to themagnetic field 16.

A sine wave 204 is provided to more clearly show the ideal behavior ofthe signal 202. The signal 202 has variations due to vertical Hallelement offsets, which tend to somewhat randomly cause element outputsignals to be too high or too low relative to the sine wave 204, inaccordance with offset errors for each element. In embodiments, theoffset signal errors may be undesirable. In some embodiments, the offseterrors can be reduced by “chopping” each vertical Hall element. Choppingwill be understood to be a process by which vertical Hall elementcontacts of each vertical Hall element are driven in differentconfigurations and signals are received from different ones of thevertical Hall element contacts of each vertical Hall element to generatea plurality of output signals from each vertical Hall element. Theplurality of signals can be arithmetically processed (e.g., summed orotherwise averaged) resulting in a signal with less offset. Chopping isdescribed more fully in U.S. Pat. No. 8,890,518 (filed Jun. 8, 2011),which is incorporated here by reference in its entirety.

Full operation of the CVH sensing element 12 of FIG. 1 and generation ofthe signal 202 of FIG. 2 are described in more detail in theabove-described PCT Patent Application No. PCT/EP2008/056517, entitled“Magnetic Field Sensor for Measuring Direction of a Magnetic Field in aPlane,” filed May 28, 2008, which is published in the English languageas PCT Publication No. WO 2008/145662, and is incorporated here byreference.

As will be understood from PCT Patent Application No. PCT/EP2008/056517,groups of contacts of each vertical Hall element can be used in amultiplexed or chopped arrangement to generate chopped output signalsfrom each vertical Hall element. Thereafter, a new group of adjacentvertical Hall element contacts can be selected (i.e., a new verticalHall element), which can be offset by one or more elements from theprior group. The new group can be used in the multiplexed or choppedarrangement to generate another chopped output signal from the nextgroup, and so on.

Each step of the signal 202 can be representative of a chopped outputsignal from one respective group of vertical Hall element contacts,i.e., from one respective vertical Hall element. However, in otherembodiments, no chopping is performed and each step of the signal 202 isrepresentative of an unchopped output signal from one respective groupof vertical Hall element contacts, i.e., from one respective verticalHall element. Thus, the graph 502 is representative of a CVH outputsignal with or without the above-described grouping and chopping ofvertical Hall elements.

It will be understood that, using techniques described above in PCTPatent Application No. PCT/EP2008/056517, a phase of the signal 502(e.g., a phase of the signal 204) can be found and can be used toidentify the pointing direction of the magnetic field 16 of FIG. 1relative to the CVH sensing element 12.

Referring now to FIG. 3 a magnetic field sensor 300 includes a sensingportion 302 and a signal processing portion 306. The sensing portion 302can include (among other things) a CVH sensing element 304, an amplifier308, and an analog-to-digital converter (“ADC”) 310. CVH sensing element304 may be the same as or similar to CVH sensing element 12 in FIG. 1.In some embodiments there are thirty-two vertical Hall elements in theCVH sensing element 304 and a corresponding thirty-two CVH sensingelement contacts. In other embodiments there are sixty-four verticalHall elements in the CVH sensing element 304 and a correspondingsixty-four CVH sensing element contacts. In yet other embodiments, anynumber of vertical Hall elements and CVH sensing element contacts may beemployed.

One skilled in the art will recognize that the grouping of elements intosensing portion 302 and signal processing portion 306 are arbitrarygroupings made for the purposes of illustration. In embodiments, theelements can be grouped or not grouped in any way.

In embodiments, ADC 310 is a sigma-delta converter and converted signal314 is a delta-modulated waveform (e.g. a bit-stream) representing theoutput of CVH sensing element 304. For example, recalling that signal202 in FIG. 2 represents the output of CVH sensing element 10 undercertain circumstances, converted signal 314 could be a delta-modulatedversion of signal 202 and may also represent the output of a CVH sensingelement such as CVH sensing element 304.

A magnet (not shown) can be disposed proximate to the CVH sensingelement 304, and can be coupled to a target object (not shown). Themagnet can be the same as or similar to the magnet 14 of FIG. 1.

Magnetic field sensor 300 may be configured to detect the position,rotational angle, speed, direction, and/or other states of a rotatingmagnetic target by, for example, measuring and processing the phase andchanges in phase of converted signal 314.

As described above, the CVH sensing element 304 can have a plurality ofvertical Hall elements, each vertical Hall element comprising a group ofvertical Hall element contacts (e.g., five vertical Hall elementcontacts), of which the vertical Hall element contact is but oneexample.

In some embodiments, sequencer circuit 312 can control CVH sensingelement 304 by switching individual vertical Hall elements and contactson and off to provide sequential CVH differential output signal 316.

In certain embodiments, output signal 316 is a differential signal. Inother embodiments, output signal 316 may be a non-differential signal.

The CVH output signal 316 may be comprised of sequential output signalstaken one-at-a-time around the CVH sensing element 304, where eachoutput signal is generated on a separate signal path and switched by thesequencer circuit 312 into the path of output signal 316. The CVH outputsignal 316 can be represented as a switched set of CVH output signalsx_(n)=x₀ to x_(N−1), taken one at a time, where n is equal to a verticalHall element position (i.e., a position of a group of vertical Hallelement contacts that form a vertical Hall element) in the CVH sensingelement 304, and where there are N such positions.

Signal processing portion 306 may employ a quadrature modulationprocessing scheme to detect phase and phase changes in converted signal314. Signal processing portion 306 may include a first modulator circuit320 and a second modulator circuit 320. The modulator circuits 320 and322 may modulate signal 314 to produce modulated signal 324 andmodulated signal 326 respectively. Taken together, the modulators 320,322 are referred to here as an I/Q modulator or as a quadraturemodulator circuit.

In an embodiment, modulated signal 324 and modulated signal 326 may beninety degrees out of phase from each other. For example, modulatorcircuit 320 may modulate converted signal 314 by applying (e.g.multiplying by) a cosine signal (e.g., cos(2nf_(CVH)t) and modulatorcircuit 322 may modulate converted signal 314 by applying (e.g.multiplying by) a sine signal (e.g., sin(2nf_(CVH)t). Because sine andcosine are ninety degrees out of phase, the resulting modulated signals324 and 326 may be quadrature signals that are ninety degrees out ofphase.

In an alternate embodiment, modulator 320 may modulate converted signal314 by multiplying with a first clock signal or square wave thatrepresents the cosine function, and modulator 322 may modulate convertedsignal 314 by multiplying with a second clock signal or square wave thatrepresents the sine signal. The first and second clock signals/squarewaves may be ninety degrees out of phase from each other. One skilled inthe art will recognize that multiplying converted signal 314 by clocksignals or square waves may introduce high frequency spectral productsinto signal 324, 326. However, the high frequency spectral products canbe filtered from the signals 324, 326 by integrators 328, 330,respectively, or by low-pass or band-pass filters.

As described above, signal processing portion 306 may also include oneor more low pass filters 328, 330. Low pass filters 328, 330 receivemodulated signals 324, 326, respectively. In an embodiment, low passfilters 328, 330 may be implemented by integrator circuits. However,this is not a requirement—any type of appropriate low pass filter orband pass filter may be applied to modulated signals 324, 326. Thefiltered signals 332, 334 may then be fed into a processor circuit 336.

Processor circuit 336 may combine the filtered, quadrature signals 332,334. The combination of filtered signals 332, 334 may be used tocalculate the angle of the magnetic target detected by CVH sensingelement 304. For example, as the magnetic target moves around the Hallelements in CVH sensing element 304, the amplitude steps (see, e.g.,FIG. 2) of signal 316 will change accordingly. Changes in amplitudesteps of signal 316 result in downstream changes in amplitude steps ofthe modulated quadrature signals 324, 334. When filtered signals 332,334 are combined in the processor circuit 336, phase changes in theresulting combined signal contain information about the original changesin amplitude steps of signal 316. However, the phase changes in thecombined signal may be further processed to determine an estimated angleof the detected magnetic target.

In an embodiment, the combined signal may be a sum or product ofquadrature signals 332 and 334. As shown in FIG. 3, the processorcircuit 336 can compute an arctangent of the quotient of quadraturesignal 334 (represented by “Q”) divided by quadrature signal 332(represented by “I”). Because quadrature signal 332 is modulated with acosine signal and quadrature signal 334 is modulated with a sine signal,the quotient of quadrature signal 334 divided by quadrature signal 332may represent the tangent of the signal 316. Thus, the arctangent, orinverse tangent, calculation may produce an output signal 338 thatrepresents the estimated angle of the detected magnetic target. In anembodiment, the arctangent calculation may be performed by an arctangentalgorithm such as a CORDIC algorithm. For example, processor circuit 336may be a processor configured to execute software, firmware, and/ormicrocode instructions to perform the CORDIC algorithm. In anotherembodiment, processor circuit 336 may be a custom circuit (such as acircuit that implements a state machine, for example) configured toperform the CORDIC algorithm.

By using quadrature signals and performing the arctangent calculation,the resulting estimated angle signal may have a resolution finer than,and/or accuracy greater than, the angular spacing of the vertical Hallelements in the CVH sensing element 304. In addition to the arctangentcalculation, the processor circuit 336 can include an interpolationmodule (not shown) operable to interpolate the angle of the detectedmagnetic field to a finer degree than the angles between the Hallelements.

The sigma-delta ADC 310 may be configured so that the converted signal314 can be written as:

$\begin{matrix}{{f(t)} = {V_{D\; C} + {\sum\limits_{n \geq 1}{A_{n}\left\lbrack {{{\sin\left( {2\pi\; f_{CVH}t} \right)}{\sin\left( \alpha_{n} \right)}} + {{\cos\left( {2\pi\;{nf}_{CVH}t} \right)}\cos\;\alpha_{n}}} \right\rbrack}} + {V_{noise}(t)}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

Where f(t) represents converted signal 314, α_(n) represents the angleof the detected magnetic field and (A_(n), α_(n)) represents theharmonic offset components, V_(DC) is the DC offset of the signal, andV_(noise) is the high pass noise (e.g. waveform 402 in FIG. 4) shaped bysigma-delta ADC 310.

It is not necessary that a sigma-delta analog-to-digital converter beemployed. ADC 310 can be replaced with any type of analog-to-digitalconverter. However, the sigma-delta ADC 310 has the advantage that itmay be implemented in a relatively small silicon area, it can operate tomove noise content to higher frequencies as shown in FIG. 4, and it maynot be necessary to recover the signal from the sigma-delta bit stream.In other words, because the noise is shifted, it may not be necessary tofilter the noise prior to further processing of the signal. In otherembodiments, ADC 310 may also be a low-pass or band-pass filteringsigma-delta ADC.

The sigma-delta ADC 310 acquires many samples of the input signal 318 toproduce a stream of 1-bit codes. In an embodiment, the samplingfrequency of ADC 310 is much higher than the Nyquist frequency. Forexample, the sample rate may approach or be equal to the frequency ofthe system clock. The frequency of the system clock may range from lessthan about 5 MHz to more than about 16 MHz in a typical embodiment.

Referring to FIG. 3A, an implementation of a sigma-delta ADC 340, whichmay be the same as or similar to ADC 310, receives an analog inputsignal 342, which may be the same as or similar to signal 318. Adifference amplifier 344 compares analog input 342 to previous samplesto generate a difference or ‘delta’ signal 346. An integrator 348receives delta signal 346 and produces an integrated or ‘sigma’ signal350. Signal 350 is compared by comparator 352 to a reference voltage toproduce output signal 354. Output signal 354 is fed back into adigital-to-analog converter 356 to be converted into an analog signal358, which is provided as an input to the difference amplifier 344.

As shown in FIG. 3A, ADC 340 receives an analog input and produces adigital bit-stream output signal 354. The duty cycle of the bit-streamoutput signal 354 represents the amplitude of the analog input signal342. For example, when the amplitude of the input signal 342 is high,the duty cycle of the output signal 354 may be high and when theamplitude of the input signal 342 is low, the duty cycle of the outputsignal 354 may be low, or vice versa.

Referring to FIG. 3B, a second order ADC 360 may be the same as orsimilar to ADC 310. In the embodiment shown in FIG. 3B, ADC 360 includesa first stage having a difference amplifier 362 and an integrator 364,and a second stage having a second difference amplifier 366 and a secondintegrator 368. ADC 360 also includes a one-bit analog-to-digitalconverter 370 and a feedback loop having a one-bit digital-to-analogconverter 372. Having two integrator stages may further reduce anyin-band quantization noise in the signal caused by the analog-to-digitalconversion.

Referring again to FIG. 3, in the embodiment where converted signal 314is described by Equation 1 above, modulators 320, 322, and filters 328,330, may be configured so that, after multiplying f(t) of equation (1)by the sin and cosine signals of the modulators 320, 322 and filteringthe signal for k CVH cycles, modulated signals 332,334 can be writtenas:

$\begin{matrix}{I = {{\int_{0}^{{kT}_{CVH}}{{f(t)} \cdot {\cos\left( {2\pi\; f_{CVH}t} \right)} \cdot {dt}}} = {{{A_{1}k\;\frac{T_{CVH}}{2}{\cos\left( \alpha_{1} \right)}} + {\int_{0}^{{kT}_{CVH}}{{V_{noise}(t)} \cdot {\cos\left( {2\pi\; f_{CVH}t} \right)} \cdot {dt}}}} \cong {A_{1}k\;\frac{T_{CVH}}{2}{\cos\left( \alpha_{1} \right)}}}}} & {{Equation}\mspace{14mu} 2} \\{Q = {{\int_{0}^{{kT}_{CVH}}{{f(t)} \cdot {\sin\left( {2\pi\; f_{CVH}t} \right)} \cdot {dt}}} = {{{A_{1}k\;\frac{T_{CVH}}{2}{\sin\left( \alpha_{1} \right)}} + {\int_{0}^{{kT}_{CVH}}{{V_{nosie}(t)} \cdot {\sin\left( {2\pi\; f_{CVH}t} \right)} \cdot {dt}}}} \cong {A_{1}k\;\frac{T_{CVH}}{2}{\sin\left( \alpha_{1} \right)}}}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

Where I represents modulated signal 332 and Q represents modulatedsignal 334. From equations 3 and 4 it can be identified that the I and Qvalues, 332, 334, respectively, are DC values.

Performing an arctangent operation (i.e. the inverse of a tangentoperation) on the quotient of Q divided by I results in an estimatedangle of the magnetic field, as follows:

$\begin{matrix}{\alpha_{est} = {{\tan^{- 1}\left( \frac{Q}{I} \right)} = {{\tan^{- 1}\left( \frac{A_{1}k\;\frac{T_{CVH}}{2}{\sin\left( \alpha_{1} \right)}}{A_{1}k\;\frac{T_{CVH}}{2}{\cos\left( \alpha_{1} \right)}} \right)} = {{\tan^{- 1}\left( \frac{\sin\left( \alpha_{1} \right)}{\cos\left( \alpha_{1} \right)} \right)} = \alpha_{1}}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Referring to FIG. 4, the sigma-delta ADC 310 may act as a noise shapingelement, shifting noise in the original signal 316 to higherfrequencies. For example, the graph 400 is a frequency spectrum graphillustrating a noise shaping result of the sigma-delta ADC 310. In graph400, the horizontal axis represents frequency and the vertical axisrepresents amplitude of converted signal 314. Spectral lines 404 a, 404b, 404 c, 404 d, 404 e, etc. are representative of spectral content ofthe converted signal 314 of FIG. 3. As shown, the converted signal 314has highest amplitude spectral line 404 b at the fundamental frequencyf, which is the frequency at which the CVH sensing element 304 of FIG. 3circulates around the vertical Hall elements of the CVH sensing element304. The amplitude is lower at DC and at higher harmonics. The noise,however, is shifted by the ADC 310 to higher frequencies, as shown bywaveform 402. In an embodiment, the noise is shifted to frequenciessubstantially above the second and/or third harmonics 404 c, 404 c ofthe fundamental frequency f. This noise may subsequently be removed fromthe modulated signals 324, 326 by a low-pass filter, such as low passfilters 328, 330.

Operation of the modulators 320, 322 of FIG. 2 results in the modulatedsignals 324, 322 having different spectral content, wherein the spectralline 404 b is shifted to DC, but harmonic content remains. In anembodiment, low pass filters 328, 330 may be configured to remove thenoise and higher harmonics from modulated signals 324, 326 respectively,so that the resulting filtered signals 332, 334 contain primarilyrespective DC components.

Referring to FIG. 5, circuit 500 may perform the arctangent calculationdiscussed above. Circuit 500 receives signal 502, which may be acombined filtered quadrature signal, e.g., a combination of the filteredsignals 332, 334 of FIG. 3. In an embodiment, signal 502 may be thequotient of filtered signal 332 (as modulated with a sine signal)divided by filtered signal 334 (as modulated with a cosine signal).

Processor 504 may be configured to perform the CORDIC algorithm toperform an arctangent function on signal 502. Processor 504 may be acustom circuit, such as a custom-designed IC, a processor having amemory containing/programmed with instructions to perform the CORDICalgorithm, an FPGA or other type of programmable hardware programmed toperform the CORDIC function, etc. Circuit 500 also includes a controlunit circuit 506. The control circuit may control the processing flow bysending control signals to processor 504 and surrounding circuitry (suchas counter 508, sinc filters 510 and 512, and the various multiplexors,latches, and other circuits shown in FIG. 5). As shown, circuit 500 mayinclude one or more feedback loops to, for example, feedback the outputsignals of sinc filters 510 and 512 as inputs to processor 504. Asprocessor 504 processes input signal 502, it provides output signal 514which represents the arctangent of input signal 502.

In an embodiment, processor 504 has a dual functionality as I/Qmodulator and an arctangent calculator. Counter 508 represents the phaseof the sine and cosine reference signals (used for generating thequadrature components). The signal 502 is multiplied by these sine andcosine signals generated by processor 504. The result of suchmultiplication pass through filters 510, 512 and, when the referencesignal period is finished (as controlled by 506), control unit 506asserts a control signal that causes processor 504 to begin performingan arctangent function. When the arctangent operation is complete, thearctangent value representing the estimated angle of the target isprovided as an output (e.g. signal 514).

The CVH techniques above may produce an output signal (i.e. an estimatedangle or location of the magnetic target) each time a CVH cycle iscompleted. Each CVH cycle consists of a sampling from each of thevertical Hall elements in the CVH sensing element. For example, the CVHsensing element 10 in FIG. 1 is shown having 32 vertical Hall elements.During one CVH cycle, each vertical Hall element is activatedsequentially. The resulting signals are concatenated over time toproduce signal 316. For example, referring to FIG. 2, graph 200 showsthe output CVH sensing element 10 over time. The horizontal axis ofgraph 200 represents each Hall element in CVH sensing element 10, andthe vertical axis represents the magnetic field detected by eachsequential vertical Hall element.

Referring to FIG. 3, when a CVH cycle is complete, the signal processingportion 306 can perform an integration over the waveform produced by theCVH cycle to calculate an estimated angle. In such embodiments, theCVH-based sensor may calculate one estimated angle each time a CVH cycleis complete. Thus, to provide an accurate output of the angle, the timeto complete the CVH cycle should at least be greater than the Nyquistfrequency for sampling the target. As an example, if the target has anexpected maximum rotational frequency of F, the sampling frequency ofthe CVH-based sensor should be at least 2*F, and the corresponding timeperiod T to complete a full CVH cycle should be less than half therotational period of the magnetic target, or T<1/(2*F).

As an example, assume that CVH sensing element 10 in FIG. 1 andsequencer circuit 312 in FIG. 3 are configured so that a CVH cycleactivates Hall element 0, then Hall element 1, then Hall element 2, etc.The cycle may continue sequentially until all 32 Hall elements (numbered0 to 31 in FIG. 1) have been activated to produce signal 202 in FIG. 2.After or as the 32 samples are acquired, signal processing circuit 306can process the signal 202 (as described above) to produce an estimatedangle in output signal 338.

Turning now to FIG. 6, embodiments of the CVH-based magnetic fieldsensor may implement a windowed integration scheme. The windowedintegration scheme may produce an estimated angle on output signal 338after every N samples taken by the Hall elements in CVH sensing element10, where the number N is any integer less than or equal to the numberof Hall elements in the CVH sensing element 10.

The windowed integration scheme may begin a CVH cycle on any Hallelement. As shown in FIG. 6, a first CVH cycle 602 may begin with Hallelement 4, as shown by starting line 604. During CVH cycle 602,sequencer circuit 312 may sequentially activate and cause readings to betaken from the Hall elements 4-31, then 0-3, to produce an output signalsimilar to signal 202 in FIG. 2. (One skilled in the art may recognizethat the output signal produced by CVH cycle 602 may be phase-shifted byabout 45 degrees with respect to output signal 202 due to CVH cycle 602starting from Hall element 4 rather than Hall element 0). After CVHcycle 602 completes, the signal processing circuit can produce anestimated angle as an output.

In the next CVH cycle 606, however, it may not be necessary to waituntil CVH cycle 602 is complete before updating the output signal with anew estimated angle. Using a windowed integration scheme, a newestimated angle may be produced as soon as a sample is taken from Hallelement 5.

The beginning of CVH cycle 606, shown by start line 608, begins withHall element 5. Just prior to the beginning of CVH cycle 606, during CVHcycle 602, samples were taken from Hall elements 5-31 and then 0-4.Thus, these recent samples, along with the most recent sample from Hallelement 5, can be used to perform an integration and produce anestimated angle as the output as soon as the sample from Hall element 5is taken.

Continuing the example, the next sample may be taken from Hall element6, as shown by line 610. Just prior to taking the sample from Hallelement 6, samples were taken from Hall elements 6-31 then 0-5. Again,these recent samples, along with the most recent sample from Hallelement 6, can be used to perform an integration and produce anestimated angle as the output as soon as the sample from Hall element 5is taken. Accordingly, in this example, the estimated angle at theoutput signal can be updated every time a sample is taken from a Hallelement. Thus, using a windowed integration scheme, the rate of updatingthe output signal can be increased from 1 update every CVH cycle, to Nupdates every CVH cycle, where N is the number of Hall elements in CVHsensing element 10.

In other embodiments, using a windowed integration scheme, the CVH-basedmagnetic field sensor can update the output signal after every m Hallelements have sampled the magnetic field, where m is an arbitraryinteger less than the number of Hall elements N. For example, assume mis 4. In this case, the output signal will be updated after every 4samples are taken from the Hall elements. The first windowed integrationcycle may start with Hall element 0 and proceed to take samples fromHall elements 0-31. When the last sample is taken again from Hallelement 0, the output signal is updated with the estimated angle.

After updating the estimated angle, the CVH magnetic field sensor mayproceed to take samples from Hall elements 1-4. After taking the samplefrom Hall element 4, the output signal is updated again with a newlyestimated angle. The newly estimated angle may be based on anintegration of the most recent samples from Hall elements 5-31 and 0-4.

After again updating the estimated angle, the CVH sensor may proceed totake samples from Hall elements 5-8 and, after the sample from Hallelement 8 is taken, again update the output signal with a new estimatedangle. The CVH sensor may continue this way, providing updated outputafter every m samples are taken from the Hall elements.

One skilled in the art will recognize that m can be any arbitrarynumber, and it need not be evenly divisible into the number of Hallelements N.

Referring to FIG. 7, a CVH magnetic field sensor 700 may be configuredto perform a windowed integration scheme using techniques describedabove in conjunction with FIG. 6. The CVH magnetic field sensor 700includes a CVH sensing element 702, which may be the same as or similarto CVH sensing element 10, a variable time delay 708 controlled bycontrol circuits such as circuits 704, 706, and an ADC 710. ADC 710 maybe the same as or similar to ADC 310 in FIG. 3.

Converted signal 711 produced by ADC 710 may be the same as or similarto converted signal 314. Modulator 712 may modulate signal 711 withcosine signal 714, and modulator 716 may module signal 711 with sinesignal 718, to produce quadrature modulated signals 713, 717,respectively.

Using the sliding window technique described above in conjunction withFIG. 6, modulated signals 713 and 717 may be written as:

$\begin{matrix}{I = {{\int_{k\;\frac{T_{CVH}}{4}}^{{({1 + \frac{1}{n}})}{kT}_{CVH}}{{f(t)} \cdot {\cos\left( {2\pi\; f_{CVH}t} \right)} \cdot {dt}}} \cong {A_{1}k\;\frac{T_{CVH}}{2}{\cos\left( \alpha_{1} \right)}}}} & {{Equation}\mspace{14mu} 5} \\{Q = {{\int_{k\;\frac{T_{CVH}}{n}}^{{({1 + \frac{1}{n}})}{kT}_{CVH}}{{f(t)} \cdot {\sin\left( {2\pi\; f_{CVH}t} \right)} \cdot {dt}}} \cong {A_{1}k\;\frac{T_{CVH}}{2}{\sin\left( \alpha_{1} \right)}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

In equations 5 and 6, f(t) represents digital signal 711, I representsquadrature modulated signal 713, Q represents quadrature modulatedsignal 717, and n is a multiplier representing the increase inthroughput of the output signal. For example, in a CVH sensing elementwith 32 Hall elements (N=32), where the output is updated after every 8samples (m=8), the increase in throughput of the output signal n wouldbe n=m/N=4. Thus, in this example, where an integration is performedafter every 8 samples, the throughput of the output signal is increased4× with respect to a CVH magnetic field sensor that does not use awindowed integration scheme.

Modulated signals 713 and 717 are received by windowed integrators 720and 722. As noted above, a windowed integration scheme (e.g. usingsliding windows of samples from the Hall effect elements) may beemployed.

In an embodiment, ‘n’ in equations 5 and 6 is greater than 1 and may beas large as N, where N is the number of elements in the CVH. In thiscase, the system will update the output representing the estimated angleof the target n times during one CVH cycle. Each integration may have awindow length (e.g. a number of samples that are used to perform theintegration) equal to one CVH cycle (i.e. each integration may include Nsamples where N is the number of elements in a full CVH cycle).

In an embodiment, the system may perform an average of multipleestimated angles in order to provide an averaged estimated angle output.The average may be performed over any number of samples of the estimatedangle signal. Recall that n represents the number of times the estimatedangle signal is updated in one CVH cycle. If the average is performedover n (or fewer) samples of the estimated angle signal, the averagedestimated angle may be calculated (and/or provided as an output) at afrequency equal to or less than that of the CVH cycle (i.e.f(avg)<=1/TCVH, where f(avg) is the frequency that the averagedestimated angle is calculated, f(CVH) is the frequency of the CVHcycles. In other embodiments, the average can be performed over morethan n samples of the estimated angle signal. In this case, thefrequency of the averaged estimated angle may be greater than thefrequency of the CVH cycles.

The outputs of integrators 720 and 722 are amplified by amplifiers 724and 726, and received by arctangent processing circuit 728. Arctangentprocessing circuit 728 may be the same as or similar to processorcircuit 336 shown in FIG. 3.

The output signal 732 may represent the estimated angle of the magnetictarget. As noted above, the output may be updated more frequently thanonce every CVH cycle. In an embodiment, the output may be updated afterevery m samples taken by the Hall effect elements in CVH sensing element702, where m is an arbitrary integer less than or equal to the number ofHall effect elements in CVH sensing element 702.

All references cited in this document are incorporated by reference intheir entirety. Having described various embodiments, which serve toillustrate various concepts, structures and techniques, which are thesubject of this patent, it will now become apparent to those of ordinaryskill in the art that other embodiments incorporating these concepts,structures and techniques may be used. Accordingly, it is submitted thatthat scope of the patent should not be limited to the describedembodiments but rather should be limited only by the spirit and scope ofthe following claims.

The invention claimed is:
 1. A magnetic field sensor, comprising: acircular vertical Hall (CVH) sensing element to produce an analog signalrepresenting an external magnetic field; an analog-to-digital convertercoupled to receive the analog signal and produce a digital signal; aquadrature modulator circuit coupled to the digital signal and operableto generate a plurality of quadrature modulated signals comprising afirst modulated signal and a second modulated signal, wherein thequadrature modulator circuit comprises: a first modulator to modulatethe digital signal by applying a cosine signal to the digital signal togenerate the first modulated signal, wherein the cosine signal isassociated with a frequency associated with a duty cycle of the CVHsensing element; a second modulator to modulate the signal by applying asine signal to the digital signal to generate the second modulatedsignal, wherein the sine signal is associated with the frequencyassociated with the duty cycle of the CVH sensing element; and aprocessor stage coupled to use signals representative of the pluralityof quadrature modulated signals and operable to perform an arctangentcalculation to determine an estimated angle of the external magneticfield, wherein the processor stage comprises a circuit to perform aCoordinate Rotation Digital Computer (CORDIC) algorithm to perform thearctangent calculation on the first modulated signal and the secondmodulated signal to determine the estimated angle of the externalmagnetic field.
 2. The magnetic field sensor of claim 1 wherein thecircuit to perform the CORDIC algorithm is a processor configured toexecute instructions that cause the processor to perform the CORDICalgorithm.
 3. The magnetic field sensor of claim 2 wherein theinstructions are software instructions, firmware instructions,micro-code instructions, or a combination thereof.
 4. The magnetic fieldsensor of claim 1 wherein the arctangent calculation produces anestimated angle has an accuracy greater than a predetermined anglebetween one or more vertical Hall element contacts of the CVH sensingelement.
 5. The magnetic field sensor of claim 1 wherein theanalog-to-digital converter is a sigma-delta analog-to-digital converterand the digital signal is a pulse stream.
 6. The magnetic field sensorof claim 5 wherein the sigma-delta analog-to-digital converter comprisesa noise shaping transform that shifts quantization noise to higherfrequencies.
 7. The magnetic field sensor of claim 1 wherein theprocessor stage is further configured to perform a sliding windowintegration using the signals representative of the plurality ofquadrature modulated signals.
 8. The magnetic field sensor of claim 1wherein the processor stage is configured to perform the arctangentcalculation to compute the estimated angle at a frequency greater thanthat of a CVH cycle.
 9. The magnetic field sensor of claim 1 wherein theprocessor stage is configured to calculate a quotient of the firstmodulated signal divided by the second modulated signal.
 10. Themagnetic field sensor of claim 9 wherein the processor stage isconfigured to perform the arctangent calculation using the quotient. 11.The magnetic field sensor of claim 1, further comprising at least onefilter coupled to the quadrature modulator circuit and to the processorcircuit, the at least one filters filtering the first and secondmodulated signals from the quadrature modulator circuit prior to beingprovided to the processor circuit.
 12. The magnetic field sensor ofclaim 1, wherein the least one filter is at least one integrator, the atleast one integrator integrates the first and second modulated signalsfrom zero to a period of a CVH cycle.
 13. A method comprising: detectinga magnetic field by a circular vertical Hall (CVH) sensing element;producing, by the CVH sensing element, an analog signal representing theexternal magnetic field; converting the analog signal to a digitalsignal; generating a plurality of quadrature modulated signalscomprising a first modulated signal and a second modulates signal, thegenerating comprising: applying a cosine signal to the digital signal togenerate the first modulated signal, wherein the cosine signal isassociated with a frequency associated with a duty cycle of the CVHsensing element; and applying a sine signal to the digital signal togenerate the second modulated signal, wherein the sine signal isassociated with the frequency associated with the duty cycle of the CVHsensing element; and performing an arctangent calculation to determinean estimated angle of the external magnetic field, the performingcomprising using a Coordinate Rotation Digital Computer (CORDIC)algorithm to perform the arctangent calculation on the first modulatedsignal and the second modulated signal to determine the estimated angleof the external magnetic field.
 14. The method of claim 13 wherein theCORDIC algorithm is performed by a processor configured to executeinstructions that cause the processor to perform the CORDIC algorithm.15. The method of claim 14 wherein the instructions are softwareinstructions, firmware instructions, micro-code instructions, or acombination thereof.
 16. The method of claim 13 wherein the performingthe arctangent calculation comprises producing an estimated angle thathas an accuracy greater than a predetermined angle between one or morevertical Hall element contacts of the CVH sensing element.
 17. Themethod of claim 13 wherein converting the analog signal comprisesgenerating a sigma-delta encoded bit stream representing the analogsignal.
 18. The method of claim 17 wherein converting the analog signalcomprises applying a noise shaping transform to the analog signal thatshifts quantization noise to higher frequencies.
 19. The method of claim13 further comprising performing a sliding window integration using theplurality of quadrature modulated signals.
 20. The method of claim 19further comprising performing the arctangent calculation to compute theestimated angle at a frequency greater than that of a CVH cycle.
 21. Themethod of claim 13 further comprising calculating a quotient of thefirst modulated signal divided by the second modulated signal.
 22. Themagnetic field sensor of claim 21 wherein performing the arctangentcalculation comprises performing the arctangent calculation using thequotient.
 23. The magnetic field sensor of claim 13, further comprisingfiltering the first and second modulated signals from the quadraturemodulator circuit prior to being provided to the processor circuit. 24.The magnetic field sensor of claim 23, wherein the filtering comprisesintegrating the first and second modulated signals from zero to a periodof a CVH cycle.